Uncovered Interest Rate Parity (UIP): Definition and Calculation

What Is Uncovered Interest Rate Parity (UIP)?

Uncovered interest rate parity (UIP) theory states that the difference in interest rates between two countries will equal the relative change between their excurrency change rates over the same period. It is one form of interest rate parity (IRP) used alongside covered interest rate parity.

If the uncovered interest rate parity relationship does not hold, then there is an opportunity to make a risk-free profit using currency arbitrage or forex arbitrage. Arbitrage allows investors to profit from small price differences by simultaneously buying and selling the same asset in different markets. If UIP does hold, however, there should be no ultimate difference in these prices once exchange rates and interest rates are taken into account.

Understanding Uncovered Interest Rate Parity (UIP)

Uncovered interest rate parity is related to the "law of one price." This economic theory states that the price of an identical security, commodity, or product traded anywhere in the world should have the same price regardless of location when currency exchange rates are taken into consideration. In other words, in a global free market with no trade restrictions, the only difference in prices should come from differences in exchange rates.

When uncovered interest rate parity holds, there can be no excess return earned from simultaneously going long a higher-yielding currency investment and shorting a different lower-yielding currency investment or interest rate spread. Uncovered interest rate parity assumes that the country with the higher interest rate or risk-free money market yield will experience depreciation in its domestic currency relative to the foreign currency.

The "law of one price" exists because differences between asset prices in different locations should eventually be eliminated due to the arbitrage opportunity. The law of one price theory is the underpinning of the concept of purchasing power parity (PPP).

Purchasing power parity states that the value of two currencies is equal when a basket of identical goods is priced the same in both countries. This relates to a formula that can be applied to compare securities across markets that trade in different currencies. As exchange rates can shift frequently, the formula can be recalculated to identify mispricings across various international markets.

Formula and Calculation for Uncovered Interest Rate Parity

The formula for uncovered interest rate parity is:

$\begin{aligned} &F_0=S_0\frac{1+i_c}{1+i_b}\\ &\textbf{where:}\\ &F_0=\text{Forward rate}\\ &S_0=\text{Spot rate}\\ &i_c=\text{Interest rate in country }c\\ &i_b=\text{Interest rate in country }b \end{aligned}$​F0​=S0​1+ib​1+ic​​where:F0​=Forward rateS0​=Spot rateic​=Interest rate in country cib​=Interest rate in country b​

How to Calculate Uncovered Interest Rate Parity

Uncovered interest rate parity is based on the theory that countries with high interest rates tend to have currencies that often depreciate. This is calculated through the formula above, which takes the spot exchange rate between the two currencies and multiplies it by the interest rate in one country, divided by the interest rate in the second country. 

In theory, the expected spot exchange rate will be equal to the gap between the two countries’ interest rates.

However, if this does not materialize, investors can make a profit by taking a loan in a low-interest-rate currency and using it to purchase a high-interest-rate currency. 

Uncovered Interest Rate Parity vs. Covered Interest Rate Parity

Both uncovered and covered interest rate parity relate to risks that arise from the exchange rates between currencies.

Covered interest parity (CIP) theorizes that the relationship between the spot and forward currency values and the interest rates of two countries should be in equilibrium. Investors making use of CIP can use forward or futures contracts to cover exchange rates to hedge their market risk.

Uncovered interest rate parity (UIP) involves forecasting rates and not covering exposure to foreign exchange risk. There are no forward rate contracts, and it uses only the expected spot rate.

Limitations of Uncovered Interest Parity

The main limitation of uncovered interest rate parity is that it is theoretical. There is only limited evidence to support UIP under real-world conditions. However, economists, academics, and analysts still use it as a theoretical and conceptual framework to represent rational expectation models. UIP requires the assumption that capital markets are efficient.

Empirical evidence has shown that over the short- and medium-term, the level of depreciation of the higher-yielding currency is less than the implications of uncovered interest rate parity. Many times, the higher-yielding currency has strengthened instead of weakened.

The Bottom Line

Uncovered interest rate parity is based on the theory that foreign exchange rates smooth out the differentials between the interest rates of two different countries. However, this theory may not always hold. Macroeconomic factors, such as monetary policy, distortions in foreign exchange markets, and time horizons can affect the validity of this theory.

Under real-world conditions, market imperfections and other factors affect the movement of currencies. As a result, investors can earn money by taking a loan in a domestic currency with low interest rates and buying a foreign currency with higher rates.